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  • 1.
    Amo-Navarro, Jesus
    et al.
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Conejero, J. Alberto
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Hoyas, Sergio
    Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain..
    Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives2021In: Mathematics, E-ISSN 2227-7390, Vol. 9, no 19, article id 2508Article in journal (Refereed)
    Abstract [en]

    In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.

  • 2.
    Anjum, Asad Ur Rehman
    et al.
    Univ Engn & Technol, Dept Math, Lahore 54890, Pakistan.;Minhaj Univ, Dept Math, Lahore 54770, Pakistan..
    Chaudhry, Qasim Ali
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Univ Hail, Fac Sci, Dept Math, Hail 81451, Saudi Arabia..
    Almatroud, A. Othman
    Univ Hail, Fac Sci, Dept Math, Hail 81451, Saudi Arabia..
    Sensitivity Analysis of Mathematical Model to Study the Effect of T Cells Infusion in Treatment of CLL2020In: Mathematics, E-ISSN 2227-7390, Vol. 8, no 4, article id 564Article in journal (Refereed)
    Abstract [en]

    In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naive, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters' behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia.

  • 3.
    Ben Khedher, Nidhal
    et al.
    Univ Hail, Coll Engn, Dept Mech Engn, Hail 81451, Saudi Arabia.;Univ Monastir, Natl Sch Engn Monastir, Lab Thermal & Energet Syst Studies LESTE, Monastir 5000, Tunisia..
    Shahabadi, Mohammad
    Univ Oklahoma, Sch Aerosp & Mech Engn, Norman, OK 73019 USA..
    Alghawli, Abed Saif
    Prince Sattam Bin Abdulaziz Univ, Comp Sci Dept, Al Aflaj 11912, Saudi Arabia..
    Hulme-Smith, Christopher
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Process.
    Mehryan, Seyed Abdollah Mansouri
    Islamic Azad Univ, Yasooj Branch, Young Researchers & Elite Club, Yasuj 7591493686, Iran..
    Numerical Study of the Flow and Thermomagnetic Convection Heat Transfer of a Power Law Non-Newtonian Ferrofluid within a Circular Cavity with a Permanent Magnet2022In: Mathematics, E-ISSN 2227-7390, Vol. 10, no 15, article id 2612Article in journal (Refereed)
    Abstract [en]

    The aim of this study is to analyze the thermo-magnetic-gravitational convection of a non-Newtonian power law ferrofluid within a circular cavity. The ferrofluid is exposed to the magnetic field of a permanent magnet. The finite element method is employed to solve the non-dimensional controlling equations. A grid sensitivity analysis and the validation of the used method are conducted. The effect of alterable parameters, including the power law index, 0.7 <= n <= 1.3, gravitational Rayleigh number, 10(4) <= Ra-T <= 10(6), magnetic Rayleigh number, 10(5) <= Ra-M <= 10(8), the location of the hot and cold surfaces, 0 <= lambda <= pi/2, and the length of the magnet normalized with respect to the diameter of the cavity, 0.1 <= L <= 0.65, on the flow and heat transfer characteristics are explored. The results show that the heat transfer rate increases at the end of both arcs compared to the central region because of buoyancy effects, and it is greater close to the hot arc. The location of the arcs does not affect the heat transfer rate considerably. An increase in the magnetic Rayleigh number contributes to stronger circulation of the flow inside and higher heat transfer. When the Kelvin force is the only one imposed on the flow, it enhances the heat transfer for magnets of length 0.2 <= L <= 0.3.

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  • 4. Hosseini, Zahra Shah
    et al.
    Abidi, Awatef
    King Khalid Univ, Coll Sci Abha, Dept Phys, Abha 61421, Saudi Arabia.;Monastir Univ, Energy Engn Dept, Natl Engn Sch, Res Lab Metrol & Energy Syst, Monastir City 5000, Tunisia.;Sousse Univ, Higher Sch Sci & Technol Hammam Sousse, Sousse City 4011, Tunisia..
    Mohammadi, Sajad
    Mehryan, Seyed Abdollah Mansouri
    Islamic Azad Univ, Yasooj Branch, Young Researchers & Elite Club, Yasuj 7591493686, Iran..
    Hulme, Christopher
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Process.
    A Fully Resolved Computational Fluid Dynamics Study of the Boundary Layer Flow of an Aqueous Nanoliquid Comprising Gyrotactic Microorganisms over a Stretching Sheet: The Validity of Conventional Similarity Models2021In: Mathematics, E-ISSN 2227-7390, Vol. 9, no 21, p. 2655-, article id 2655Article in journal (Refereed)
    Abstract [en]

    When materials are processed in the form of sheets that are stretched, cooling is often required. Coolants have been developed to maximize the rate of heat transfer away from the sheet, including by adding nanoparticles and microorganisms to control the physical properties of the fluid. Such coolants perform well, but the interaction between them and the sheet is not yet fully understood. Most of the articles found in the literature have used similarity models to solve the set of governing equations. In this method, the governing equations can be mapped into a set of 1-D equations and solved easily. However, care should be taken when using this method as the validity of this method is ensured only in the fully developed region, far away enough from the extrusion slit. The present study, therefore, aims to explore the reliability of a similarity model by comparing it with a full computational fluid dynamics (CFD) approach. In this work, the boundary layer flow of a nanoliquid comprising gyrotactic microorganisms in both the developed and undeveloped regions of a stretching sheet is studied using computational fluid dynamics with the finite difference approach, implemented using FORTRAN. The results of the CFD method are compared against the similarity analysis results for the length of the developed and undeveloped regions. This study, for the first time, distinguishes between the undeveloped and fully developed regions and finds the region in which the similarity analysis is valid. The numerical results show that the critical Reynolds numbers for the boundary layers of the concentration of the nano-additives and of density of the microorganisms are equal. To achieve an agreement between the CFD and the similarity model within 5%, the Grashof number for the hydrodynamic boundary layer must be Gr < 10(5). Nonetheless, this length reduces significantly when the Grashof number increases from 10(5) to 10(6). The reduced Nusselt number, Nu(r), increases when the density difference of the microorganisms increases.

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